Preheat the oven to 400°F
Line a large baking sheet with paper towels. Set the sliced tomatoes on top in a single layer. Season the tomatoes evenly on both sides with salt and pepper, then cover with another paper towel and let sit for 15 minutes to draw moisture out of the tomatoes.
As the tomatoes sit, line a baking sheet with parchment paper and slowly roll out the puff pastry sheet. Prick the pastry sheet with a fork every few inches, leaving a 1/2-inch border.
Heat the teaspoon of olive oil over medium heat in a medium pan, then sautée the shallot until browned and set aside.
Prepare the tofu ricotta by adding the tofu, miso paste, olive oil, nutritional yeast, garlic, salt, pepper, and lemon juice to a food processor and pulse until creamy, stopping to scrape down the sides as needed. Add salt and pepper to taste, and set aside.
Layer the heirloom tomatoes and the sautéd shallot on top of the tart. Bake, for 20 minutes, remove from the oven and slowly slide the tart directly on top of the baking sheet and top it with dollops of the tofu ricotta. Return the tart to the oven for another 10 minutes, then turn the oven on high broil for 1-2 minutes and remove the tart.
Top the tart with freshly chopped basil and drizzle olive oil on top of the tart to taste. Serve warm or at room temperature.
